The light emission from a semiconductor gain region has a broader spectrum than that from a gas comprised of a single species of atom, but the strongest light emission and gain typically occur for photon energies nearly equal to the band gap energy. Therefore, when designing a semiconductor laser, we must select a material for the gain medium whose band gap energy corresponds to the photon energy (wavelength) we wish to emit.
However, there are other material selection considerations as well. As you know, semiconductor lasers are composed of crystalline semiconductors. In addition, all practical laser diodes contain heterojunctions. When fabricating a heterojunction, we must grow a semiconductor crystal on top of a different semiconductor. Different semiconductors have different lattice constants, which are the spacings between atoms. When we grow a crystal on top of a different base crystal, the new crystal attempts to use the base crystal as a template. But if the lattice constants of the two crystals are very different, this template does not match the new crystal’s preferred configuration, and the new crystal is strained as a result. Large strain leads to a high density of defects in the new crystal. Defects are a significant problem, because they exhibit undesirable electronic and optical properties. Therefore, whenever possible, we would like to ‘lattice match’ the heterojunction – in other words, we’d like to use semiconductors whose band gaps are different but whose lattice constants are nearly the same. A famous example of this is , whose band gap energy , and , whose band gap energy , both have a lattice constant . Therefore, can be grown on with very low defect densities.
The following link contains a nice table of the semiconductor material systems that are used to produce laser diodes of various wavelengths: